Construction of biorthogonal wavelet filter banks through a top-down and bottom-up dual-chain method. See paper [ChuiHanZhuang].

Given a pair of d-biorthogonal lowpass filters (a_0,a_1), the algorithm first construct a top-down dual chain a0->a1->...->ar so that ar is either with only 2 cosets or is a filter with signle tap. The bottom-up precedue then construct a bottom-up chain (ar, b_{r,1},...b_{r,{d-1}})->(a_{r-1},b_{r-1,1},...b_{r-1,d-1})->...->(a0,b_{0,1},...,b_{0,d-1}).